Ialso think this may be the PSU, my computer whistles and it seems,s when the GPU starts running for a couple of mins it see,s to enter a limp mode in that game.
Whistling can be a few things, noisy fan, leaking capacitor from either the PSU or the graphics card (gfx card more likely)
Just a quick note on that power supply although you don't mention the brand name, I'm currently using a 500w Antec (good brand) with a system roughly the same power as yours (i5 3570k stock, 7950 Asus CUII stock, 8gb Corsair Dominator, Asus P8H77-V and a few hard drives) as my current one is being RMA'd and I also get a slight whistling whilst starting FIFA 13 and all my games have had slight flickering, symptoms of not enough power to the GPU. Just throwing that in there in case you have a non branded PSU for future reference.
I would do exaclty as scout_03 has said, check the GPU if its fine in someone elses computer, if thats ok and it passes 3d mark then run something like this on your friends computer http://mikelab.kiev.ua/index_en.php?page=PROGRAMS/vmt_en
To check the all of the VRAM is all ok and working.